1 Suppose the failure time history of a component is given (where downward -facing arrows indicate failure times):

a Assume the failure process follows a NHPP with ?(t) = exp(?+?t) Estimate the model parameters ? and ? using the MLE

b What is the expected number of failures from the current time until 72 months?

c Check if the failure process has a time trend [? = 01] If it does not, find the ROCOF

2 Suppose the following data were observed in a repairable system:

a Assume the failure process follows a renewal process and the interarrival time have

Estimate the parameter ? based on the failure data (Hint: find the MLE)

b Now, assume that the failure process follows a renewal process with an exponentially distributed interarrival time Estimate the value of ?